2019/01/21 by Matheus Brito, Vyjayanthi Chari, Brito, Matheus +1
Mathematics · #13F60 #17B37 #20G42 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1901.07020
openalex publication_date 2019/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study certain monoidal subcategories (introduced by David Hernandez and Bernard Leclerc) of finite--dimensional representations of a quantum affine algebra of type A. We classify the set of prime representations in these subcategories and give necessary and sufficient conditions for a tensor product of two prime representations to be irreducible. In the case of a reducible tensor product we describe the prime decomposition of the simple factors. As a consequence we prove that these subcategories are monoidal categorifications of a cluster algebra of type A with coefficients.